Numerical studies of lasing and electromagnetic fluctuations in open complex systems

This dissertation explores lasing behavior and the effects of electromagnetic fluctuations in open complex systems in one dimension. It consists of three topics: thermal electromagnetic field fluctuations in open passive systems, fluctuations due to atomic interactions with external reservoirs in open active systems, and spatially nonuniform gain distributions in open systems.;Numerical models which do not require prior knowledge of cavity modes are developed to simulate fluctuations which must accompany associated dissipations. First, thermal noise is simulated in open cavities due to output coupling. The absorbing boundary of the numerical grid is treated as a blackbody which emits thermal radiation that penetrates the cavity. It is demonstrated that in the non-Markovian regime, the buildup of intracavity field noise depends on the ratio of the cavity field lifetime to the coherence time of thermal radiation. Second, fluctuations which accompany the dephasing of atomic polarization and the change of the excited state's population are simulated in dielectric slab lasers and random lasers. This method is based on the Maxwell-Bloch equations for two-level atoms with real noise terms derived from stochastic c-number evolution equations. In random lasers, noise is found to influence lasing thresholds. In the transition from amplified spontaneous emission to clear lasing oscillation, spectral narrowing around mode frequencies is observed. Discrete lasing peaks are found to manifest themselves more clearly with partial pumping even when noise is included.;This leads to a study of the effects of optical gain nonuniformly distributed in random systems. It is demonstrated that even without gain saturation and mode competition, the spatial nonuniformity of gain can cause dramatic and complicated changes to lasing modes. Mode mixing increases as the gain distribution changes gradually from uniform to nonuniform. Furthermore, new lasing modes are created by nonuniform gain distributions. They may disappear together with existing lasing modes, thereby causing fluctuations in the local density of lasing states. Some new lasing modes are examined in detail and found to exhibit high output directionality, meaning random laser properties may be modified significantly without changing the underlying structures.